Hey Kathy, thanks for your email. It sounds like you already have a lot of the important pieces of deadlifting success outlined here.
Like you mentioned, I think accessory work like abs and reverse hypers are great for keeping the midline strong. But just as you said, doing more deadlifts is the best way to fix any issues you have with the movement, and will also greatly improve that core strength.
I realize you may be hesitant to pile on more deadlifts since you have been experiencing pain from them. I know from my own experience with chronic lower back soreness after deadlifting that my position and mechanics were the main cause for the discomfort. I had been deadlifting heavy since high school and had always just dealt with being sore for days after. For me, all it took was lowering my hips a bit in the set-up and getting more of my weight behind the bar.
By lowering my hips I was able to use my legs more in the initial pull from the ground. While my hamstrings were loaded, my hips were always so high that I didn’t get much help from my quads so my lower back ended up having to do more of the work. Once I turned the initial pull into more of a leg press action, driving my chest up simultaneously with my hips I no longer had any lingering back soreness after deadlifting.
I also learned how to pull myself into position and get more of my bodyweight behind the bar before starting the pull. This allowed me to use my bodyweight as a crane to pull the weight up and I also found it much easier to maintain tension through my abs, erectors and lats. Everything was engaged before I even started to pull so I was able to transmit more force into making the bar move.
Good luck to you and I hope you can begin to deadlift (low-back)pain-free!